1. Field of the Invention
This invention relates to a digital filter and, more particularly, to a digital filter of the kind for computing the sum of or a difference between a plurality of different samples having respective coefficients each of which is less than 1.
2. Description of the Related Art
The video signals have recently become capable of representing image information in a higher degree of definition. In the case of TV signals, for example, the conventional signals of the NTSC system or the like are being replaced with HDTV (high-definition TV) signals. In transmitting the high-definition image signals through a recording medium such as a tape or a disc, a communication satellite, an optical fiber, or the like that can be regarded as a transmission route in a broad sense of the word, they are preferably transmitted in a coded state by changing them from an analog signal form into a digital signal form, because their image quality can be thus prevented from being deteriorated by S/N, jitters, etc.
Meanwhile, in cases where the bandwidth of the video signal is desired to be, for example, at least 30 MHz, the sampling must be accomplished at a rate of at least 60 MHz in accordance with the sampling theorem. Therefore, assuming that the signal is analog-to-digital (A/D) converted at a rate of 74.25 MHz with 8 bits, the transmission rate then becomes (74.25 (MHz).times.8 (bit)=) 594 M bits/s, which is a great amount of information.
If the digital signal of such a great amount of information is transmitted as it is, it would exceed the currently conceivable capacity of a single channel transmission route. To solve this problem, varied methods for compressing the great amount of information have been proposed. These methods include a sub-sampling method.
FIG. 1 of the accompanying drawings shows one example of the sub-sampling method. In FIG. 1, marks "x" and "o" respectively denote picture elements. The mark "x" denotes the picture elements to be omitted by the sub-sampling. The mark "o" denotes the picture elements to be actually transmitted. Reference symbols n, n-1 and n-2 represent scanning line numbers. The signal transmission is carried out in the order of the scanning line numbers n-2, n-1 and n. This method is called a line offset sub-sampling method. As shown in FIG. 1, only the picture elements of each line that are in positions deviating by one picture element from the picture elements of another line are transmitted. Accordingly, the information amount is compressed to 1/2.
FIG. 2 is a block diagram showing in outline the arrangement for sub-sampling a video signal. Referring to FIG. 2, a terminal 1 is arranged to receive an analog video signal. An analog low-pass filter 2 is arranged to limit the frequency band of the input video signal to a band which is not greater than 1/2 of the sampling frequency of an A/D converter 3. A digital spatial filter 4 is arranged to prevent any disturbance from being caused by an aliasing component produced at the time of the sub-sampling. A reference numeral 5 denotes a sub-sampling circuit. A terminal 6 is arranged to output the sub-sampled video signal.
FIGS. 3(A) and 3(B) are diagrams for explaining signals output from parts of FIG. 2. FIG. 3(A) shows picture elements output from the A/D converter 3. FIG. 3(B) shows picture elements output from the sub-sampling circuit 5. In the arrangement shown in FIG. 2, the digital spatial filter 4 is very important as it determines the picture quality of the video signal after the sub-sampling.
FIG. 4 is a diagram for explaining a computation example of the conventional digital spatial filter. In FIG. 4, reference symbols x1 to x6 respectively denote the sampled values of the picture elements. Symbols n, n-1 and n-2 denote adjacent scanning lines. In the case of this example, a value x6 which results from a filtering action on the picture element related to the sampled value x6 can be obtained from the following computing formula: ##EQU1## wherein K1 to K5 respectively represent positive coefficients and al represents a positive constant.
With such a computing operation performed for each of the picture elements, filtering can be carried out on the digital video signal. FIG. 5 shows by way of example the details of the digital spatial filter which processes the digital video signal by performing a computing operation in accordance with the formula shown above.
Referring to FIG. 5, an input terminal 11 is arranged to receive the digital video signal. Reference numerals 12a to 12n, 12p and 12q denote delay circuits for delaying the signal for one sampling period. Numerals 13a and 13b denote delay circuits 13a and 13b for delaying the signal for one line period. Numerals 14a to 14i denote adders. A numeral 15 denotes a subtracter. Numerals 16a to 16e are multipliers for performing a multiplying operation by using the respective coefficients K1 to K5. A numeral 17 denotes a divider for performing a dividing operation by using a constant al. An output terminal 18 is arranged to output a filtered digital video signal.
If the digital signal supplied to the filter of FIG. 5 consists of eight bits, the digital signal output from the filter would be of eight bits. However, the number of bits is increased by a carry which takes place at each part of the filter.
For example, in the case of a digital spatial filter in which K1=16, K2=31, K3=57, K4=8, K5=128 and al=256, the maximum value and the number of necessary bits at each of parts (A), (B), (C), (D), (E), (F), (G) and (M) are shown below:
______________________________________ maximum value number of necessary bits ______________________________________ (A) 32640 15 (B) 4080 12 (C) 36720 16 (D) 29070 15 (E) 15810 14 (F) 44880 16 (G) 81600 17 (M) 16320 14 ______________________________________
With the number of bits increased in this manner at each part of the filter, the computing speed of each computing device decreases accordingly. As a result, for a video signal sampled at a speed higher than 60M Hz, the length of time required for the computing operation would become longer than one sampling period. Under such a condition, the filtering process would be impossible.
Further, in the case of the conventional spatial filter described above, to facilitate digital computation, the divisor al of the divider 17 is set at a value which is a power of 2. The divider 17 is simply composed of a bit shift circuit. Therefore, the output of the divider 17 is obtained by carrying out a round-down process (disregarding fraction) on the input of the divider 17. As a result of the round-down process, there arises an error of about one level in the output of the divider 17. This error causes some deterioration of information. Further, in a case where the spatial filters are arranged in a multi-stage connection the information is seriously affected by the propagation and accumulation of this error.